1. **State the problem:** We are given a polynomial $$x^2 + ax + 1$$ and told it has only real zeros. We need to find the minimum value of $$a^2$$. 2. **Recall the condition for real zeros:** A quadratic polynomial $$x^2 + bx + c$$ has real zeros if and only if its discriminant $$\Delta = b^2 - 4c \geq 0$$. 3. **Apply the discriminant condition:** For our polynomial, $$b = a$$ and $$c = 1$$, so $$\Delta = a^2 - 4 \times 1 = a^2 - 4 \geq 0$$. 4. **Solve the inequality:** $$a^2 - 4 \geq 0 \implies a^2 \geq 4$$. 5. **Find the minimum value of $$a^2$$:** Since $$a^2$$ must be at least 4, the minimum value is $$\boxed{4}$$. **Final answer:** The minimum value of $$a^2$$ is 4.